Analytic shock

Shocks in fluids result from fluid flow that is more rapid than the speed of
a compression wave. Thus there is no means for the flow to adjust gradually.
Pressure, velocity, and temperatures change abruptly, causing severe fatigue
and component destruction in military aircraft and engine turbines. This
problem is not limited to supersonic aircraft; many parts of subsonic craft are
supersonic.

In what follows, we draw on these techniques to model contagion stemming from unexpected
shocks in complex nancial networks with arbitrary structure, and then use numerical
simulations to illustrate and clarify the intuition underpinning our analytical results. Our
framework explicitly accounts for the nature and scale of aggregate and idiosyncratic shocks and
allows asset prices to interact with balance sheets.

In what follows, we construct a simple nancial system involving entities with interlocking
balance sheets and use these techniques to model the spread and probability of contagious default
following an unexpected shock, analytically and numerically.
Unlike the generic, undirected
graph model of Watts (2002), our model provides an explicit characterisation of balance sheets,
making clear the direction of claims and obligations linking nancial institutions. It also includes
asset price interactions with balance sheets, allowing the effects of asset-side contagion to be
clearly delineated.